A SIMPLIFIED COMPUTATIONAL MODEL FOR MICROPLATES BASED ON A MODIFIED COUPLE STRESS THEORY

2019 ◽  
Vol 17 (5) ◽  
pp. 483-505
Author(s):  
Shengqi Yang ◽  
Shutian Liu ◽  
Liyong Tong
Keyword(s):  
Computational Model ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Modified Couple Stress

Size-dependent free vibration analysis of a three-layered exponentially graded nano-/micro-plate with piezomagnetic face sheets resting on Pasternak’s foundation via MCST

2017 ◽  
Vol 22 (1) ◽  
pp. 55-86 ◽  
Author(s):  
Mohammad Arefi ◽  
Masoud Kiani ◽  
Ashraf M Zenkour
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Modified Couple Stress ◽  
Material Length Scale ◽  
Material Length ◽  
Exponentially Graded

The present work is devoted to the free vibration analysis of elastic three-layered nano-/micro-plate with exponentially graded core and piezomagnetic face-sheets using the modified couple stress theory. To capture size-dependency for a nano-/micro-sized rectangular plate, the couple stress theory is used as a non-classical continuum theory. The rectangular elastic three-layered nano-/micro-plate is resting on Pasternak’s foundation. The present model contains one material length scale parameter and can capture the size effect. Material properties of the core are supposed to vary along the thickness direction based on the exponential function. The governing equations of motion are derived from Hamilton’s principle based on the modified couple stress theory and first-order shear deformation theory. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually the natural frequency is scrutinized for different side length ratio, thickness ratio, inhomogeneity parameter, material length scale, and parameters of foundation numerically.

Dynamic stiffness formulation for a micro beam using Timoshenko–Ehrenfest and modified couple stress theories with applications

2021 ◽  
pp. 107754632110482
Author(s):  
J Ranjan Banerjee ◽  
Stanislav O Papkov ◽  
Thuc P Vo ◽  
Isaac Elishakoff
Keyword(s):  
Free Vibration ◽  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Dynamic Stiffness ◽  
Modified Couple Stress Theory ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Stress Theory ◽  
Modified Couple Stress

Several models within the framework of continuum mechanics have been proposed over the years to solve the free vibration problem of micro beams. Foremost amongst these are those based on non-local elasticity, classical couple stress, gradient elasticity and modified couple stress theories. Many of these models retain the basic features of the Bernoulli–Euler or Timoshenko–Ehrenfest theories, but they introduce one or more material scale length parameters to tackle the problem. The work described in this paper deals with the free vibration problems of micro beams based on the dynamic stiffness method, through the implementation of the modified couple stress theory in conjunction with the Timoshenko–Ehrenfest theory. The main advantage of the modified couple stress theory is that unlike other models, it uses only one material length scale parameter to account for the smallness of the structure. The current research is accomplished first by solving the governing differential equations of motion of a Timoshenko–Ehrenfest micro beam in free vibration in closed analytical form. The dynamic stiffness matrix of the beam is then formulated by relating the amplitudes of the forces to those of the corresponding displacements at the ends of the beam. The theory is applied using the Wittrick–Williams algorithm as solution technique to investigate the free vibration characteristics of Timoshenko–Ehrenfest micro beams. Natural frequencies and mode shapes of several examples are presented, and the effects of the length scale parameter on the free vibration characteristics of Timoshenko–Ehrenfest micro beams are demonstrated.

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